Well LPI is just an umbrella term. It merely indicates the effort to reduce detectability of RF emissions and this can be achieved by various means. Frequent changes of the signal characteristics such as frequency (frequency hopping) at best occuring randomley, meaning that those signals can't be identified by repeating patterns, power managing the signal to avoid unnecessary poweroutputs, focussing emissions in areas of interest etc. all reduce detectability. If there aren't repeating patterns and just small transmissions, at best multiple at once at different frequencies the receiver might be overfed as it simply can't scope with so many signals and as there is no pattern which can be identified the software/algorithms of some RWR's must just sort out the signals as it can't adquately process them or discards it as background noise. LPI is not an AESA inherent design feature, but agile beam steering and the ability to focus narrow beams at a target or use even multiple beams at once offers opportunities which can't be provided by a mechanically scanning radar. MSA radars can still incoorperate LPI techniques, but not to the extend of an AESA radar.
Regarding missile seekers the problem is that missiles are small and AESA radars are heavier, more power hungry and have higher cooling demands, this might be problematic. And for a one shot situation it might not even be worth the effort, but I could imagin that AESA radar seekers will find their way into missiles, not for LPI characteristics, but to increase the range performance and counter measures resistence. Wether this is possible right now, I have my doubts, but don't know it for sure. But such tech is getting more efficient, smaller and lighter.